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The role of the variational formulation in the dimensionally-heterogeneous modelling of the human cardiovascular system

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Modeling of Physiological Flows

Part of the book series: MS&A — Modeling, Simulation and Applications ((MS&A,volume 5))

Abstract

The modelling of the cardiovascular system entails dealing with different phenomena pertaining to different time, constitutive and geometrical scales. Specifically, the problem of integrating various geometrical scales can be understood from a kinematical point of view, which means to integrate models with different kinematics, and in particular different dimensionality. In this context, all the variational machinery can be employed to derive consistent variational formulations according to the underlying kinematical hypotheses that rule over the corresponding models. In this work we discuss the application of variational formulations to model the blood flow in the cardiovascular system making use of heterogeneous representations. Two examples of applications are used to show the capabilities and potentialities of the present approach.

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Acknowledgements

This work was partially supported by the Brazilian agencies CNPq and FAPERJ. The support of these agencies is gratefully acknowledged.

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  1. LNCC — National Laboratory for Scientific Computing and INCT-MACC — National Institute of Science and Technology in Medicine Assisted by Scientific Computing, Av. Getúlio Vargas 333, Quitandinha, 25651-075, Petrópolis, RJ, Brazil

    Pablo J. Blanco & Raúl A. Feijóo

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  1. Pablo J. Blanco
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  2. Raúl A. Feijóo
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Correspondence to Raúl A. Feijóo .

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  1. MOX - Department of Mathematics, Politecnico di Milano, Italy

    Davide Ambrosi  & Alfio Quarteroni  & 

  2. Mathematics Institute of Computational Science and Engineering, École Polytechnique Fédérale de Laussane, Switzerland

    Alfio Quarteroni  & Gianluigi Rozza  & 

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Blanco, P.J., Feijóo, R.A. (2012). The role of the variational formulation in the dimensionally-heterogeneous modelling of the human cardiovascular system. In: Ambrosi, D., Quarteroni, A., Rozza, G. (eds) Modeling of Physiological Flows. MS&A — Modeling, Simulation and Applications, vol 5. Springer, Milano. https://doi.org/10.1007/978-88-470-1935-5_9

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